Question

Simplify the following, using only positive exponents. Do not evaluate.

Exponetial functions
c)
f^3 g−^1/f^2 g^3


d)
(k^−2m^3n)×(kmn^5)÷(k^− 1m^2 n)

Answer 1

just add powers for multipliers, subtract for divisors.

f^3 g^-1 / f^2g^3 = f^(3-2) g^(-1-3) = f^1 g^-4 = f/g^4

(k^−2m^3n)×(kmn^5)÷(k^− 1m^2 n)
= k^(-2+1-(-1)) m^(3+1-2) n^(1+5-1)
= k^0 m^2 n^5
= m^2 n^5